Multichannel active-space embedding of atomic multiplets in plane-wave DFT/PAW for core-level spectroscopies
We introduce an active-space embedding framework for core-level spectroscopies that connects localized atomic multiplets to continuum resonances within a plane-wave DFT/PAW description. The approach is complementary to widely used core-level Bethe--Salpeter implementations based on a two-particle (core-exciton) picture with typically static screening: here a correlated multiplet manifold of the absorber (including the core hole and open-shell configurations) is coherently coupled to a plane-wave photoelectron, enabling a unified treatment of localized multiplet structure and continuum lineshapes. Spectra are computed in a general time-domain formulation equivalent to Fermi's golden rule: a transition operator tailored to the specific spectroscopy technique is applied to the correlated ground state to generate an excited wavepacket, and the corresponding wavepacket autocorrelation function is evaluated without explicit real-time propagation, using Lanczos tridiagonalization or the kernel polynomial method; the spectral intensity follows from its Fourier representation. We validate the method at the Ce \(N_{4,5}\) edges, reproducing in quantitative agreement with experiment both high-\(Q\) multiplet features and the low-\(Q\) giant dipole resonance continuum, including a characteristic low-energy shoulder relevant for robust Ce valence assignments. The implementation is available open-source within the Quantum ESPRESSO XSPECTRA package (xspectruplet mode), together with reproducible inputs and scripts.